Loading

afs_orig = read.csv("MGRB_GnomAD_SweGen_cancer_UKBB_AFs_outerjoined_ss-auto-gwas-snps_hcr.csv.xz", stringsAsFactors = FALSE, header = TRUE)
models_orig = read.csv("../data/manual_polygenic_scores.hcr_tag_rescued.csv", stringsAsFactors = FALSE, header = TRUE)

# Key allele frequencies by VID
afs_orig$vid = paste(afs_orig$chrom, afs_orig$pos, afs_orig$ref, afs_orig$alt, sep = ":")
afs_orig = afs_orig[,!(colnames(afs_orig) %in% c("chrom", "pos", "ref", "alt"))]

# Add gnomad AFs to the models for imputation of missing variants
temp.gnomad_af = (afs_orig$nAA_gnomad*2 + afs_orig$nRA_gnomad) / (2*(afs_orig$nAA_gnomad + afs_orig$nRA_gnomad + afs_orig$nRR_gnomad))
models_orig$aaf = temp.gnomad_af[match(models_orig$vid, afs_orig$vid)]

# Create a full UKBB cohort by combining the age-stratified numbers
afs_orig$nRR_ukbb = afs_orig$nRR_ukbb_0_55 + afs_orig$nRR_ukbb_55_60 + afs_orig$nRR_ukbb_60_65 + afs_orig$nRR_ukbb_65_70 + afs_orig$nRR_ukbb_70_75 + afs_orig$nRR_ukbb_75_inf
afs_orig$nRA_ukbb = afs_orig$nRA_ukbb_0_55 + afs_orig$nRA_ukbb_55_60 + afs_orig$nRA_ukbb_60_65 + afs_orig$nRA_ukbb_65_70 + afs_orig$nRA_ukbb_70_75 + afs_orig$nRA_ukbb_75_inf
afs_orig$nAA_ukbb = afs_orig$nAA_ukbb_0_55 + afs_orig$nAA_ukbb_55_60 + afs_orig$nAA_ukbb_60_65 + afs_orig$nAA_ukbb_65_70 + afs_orig$nAA_ukbb_70_75 + afs_orig$nAA_ukbb_75_inf
afs_orig$nmissing_ukbb = afs_orig$nmissing_ukbb_0_55 + afs_orig$nmissing_ukbb_55_60 + afs_orig$nmissing_ukbb_60_65 + afs_orig$nmissing_ukbb_65_70 + afs_orig$nmissing_ukbb_70_75 + afs_orig$nmissing_ukbb_75_inf

# Convert afs from wide to long format
library(reshape2)
afs_long = melt(afs_orig, id.vars = c("rsid", "negstrand", "vid"), value.name = "count")
afs_long$cohort = gsub("^n(RR|RA|AA|missing)_", "", afs_long$variable)
afs_long$variable = gsub("_.*", "", afs_long$variable)
afs = dcast(afs_long, vid + rsid + negstrand + cohort ~ variable, value.var = "count")
afs = afs[,c("vid", "rsid", "negstrand", "cohort", "nRR", "nRA", "nAA", "nmissing")]

# Exclude ASRB samples -- prelim examination suggests they are rather
# poor quality, and we are not interested in their PRS distributions
# anyway.  Also exclude the various MGRB filtration options, as they
# apply only to rare variants.  Exclude SweGen as we don't have a good
# HQ bed for it.
cohorts.sel = c("mgrborig", "gnomad", "ukbb")
cohorts.main = c("mgrborig", "gnomad", "ukbb")
afs = afs[afs$cohort %in% cohorts.sel,]

Model selection

Choose polygenic models with at least 10 loci, with the exception of ShortLifespan:Deelen:10.1093/hmg/ddu139 (only six loci passing filters). For cancers, choose polygenic models only for cancers with a positive control cohort. In the case of multiple models for the same disorder, choose the most recent original publication where possible (ie exclude “meta” signatures if a good original report is available).

# Excluded due to insufficient size:
    # "CancerOfBladder:Fritsche:10.1016/j.ajhg.2018.04.001",
    # "LymphoidLeukemiaAcute:Fritsche:10.1016/j.ajhg.2018.04.001",
    # "LymphoidLeukemiaChronic:Fritsche:10.1016/j.ajhg.2018.04.001",
    # "MalignantNeoplasmOfTestis:Fritsche:10.1016/j.ajhg.2018.04.001",
    # "NonHodgkinsLymphoma:Fritsche:10.1016/j.ajhg.2018.04.001",
    # "PancreaticCancer:Fritsche:10.1016/j.ajhg.2018.04.001",
    # "APOE_rs429358:NA:NA",
    # "ShortHealthspan:Zenin:10.1038/s42003-019-0290-0",
    # "Deelen2019_90_disc",
    # "Deelen2019_99_disc",
# Excluded because a better alternative was available
    # "CancerOfProstate:Fritsche:10.1016/j.ajhg.2018.04.001",
    # "ColorectalCancer:Fritsche:10.1016/j.ajhg.2018.04.001",
    # "MelanomasOfSkin:Fritsche:10.1016/j.ajhg.2018.04.001",
    # "BreastCancer:Li:10.1038/gim.2016.43",
    # "BreastCancerFemale:Fritsche:10.1016/j.ajhg.2018.04.001",
    # "ShortParentalLifespan:Pilling:10.18632/aging.101334",
# Excluded because of issues with population-specific alleles between UK and European popns
    # "BasalCellCarcinoma:Chahal:10.1038/ncomms12510",
    # "BasalCellCarcinoma:Fritsche:10.1016/j.ajhg.2018.04.001",
# Excluded as superseded by Timmers / Pilling studies:
    # "Deelen2014_85_rep",
    # "Deelen2014_85_disc",
    # "Deelen2014_90_rep",
    # "Deelen2014_90_disc",

models.sel = c(
    "AF:Lubitz:10.1161/CIRCULATIONAHA.116.024143",
    "DiastolicBP:Warren:10.1038/ng.3768",
    "EOCAD:Theriault:10.1161/circgen.117.001849",
    "PulsePressure:Warren:10.1038/ng.3768",
    "SystolicBP:Warren:10.1038/ng.3768",

    "AlzheimersDisease:Lambert:10.1038/ng.2802",
    "ShortHealthspan:Zenin:10.1038/s42003-019-0290-0",
    "ShortParentalLifespan:Timmers:10.7554/eLife.39856",

    "Height:Wood:10.1038/ng.3097",

    "BreastCancer:Michailidou:10.1038/nature24284",
    "ColorectalCancer:Schumacher:10.1038/ncomms8138",
    "Melanoma:Law:10.1038/ng.3373",
    "ProstateCancer:Hoffmann:10.1158/2159-8290.CD-15-0315"

)
models = models_orig[models_orig$id %in% models.sel,]

Variant filtering and imputation

# Drop variants with low genotyping rate in any cohort in which that
# variant was detected.  Use the threshold of 97% genotyping rate
library(plyr)
temp.lowgt = ddply(afs[!is.na(afs$nRR),], .(cohort), function(d) mean(d$nmissing / (d$nRR + d$nRA + d$nAA + d$nmissing) >= 0.03))
temp.lowgt

##     cohort           V1
## 1   gnomad 1.596488e-03
## 2 mgrborig 8.066142e-05
## 3     ukbb 5.066883e-02

# The UKBB samples have rather a lot of dropouts here: ~ 5% of loci
# have a gt rate under 97%.

temp.gt_rate = 1 - daply(afs[!is.na(afs$nRR),], .(vid), function(d) {
    d = d[d$cohort %in% cohorts.main,]
    max(d$nmissing / (d$nRR + d$nRA + d$nAA + d$nmissing))})
mean(temp.gt_rate < 0.97)

## [1] 0.04621999

afs = afs[afs$vid %in% names(temp.gt_rate)[temp.gt_rate >= 0.97],]
mean(models$vid %in% names(temp.gt_rate)[temp.gt_rate >= 0.97])

## [1] 0.9481481

# ~5.0% of model loci lost by this filter
models = models[models$vid %in% names(temp.gt_rate)[temp.gt_rate >= 0.97],]

# Create a set of AFs for variants that have VCF entries in every cohort.  
# Note that given the relatively small size of some cohorts, this tends to 
# preferentially exclude rare variants from consideration, and will probably 
# attenuate the GRS differences.
afs.nmissing_per_cohort = tapply(is.na(afs$nRR[afs$cohort %in% cohorts.main]), afs$vid[afs$cohort %in% cohorts.main], sum)
afs.nomissing = afs[!(afs$vid %in% names(afs.nmissing_per_cohort[afs.nmissing_per_cohort > 0])),]
nrow(afs.nomissing) / nrow(afs)

## [1] 0.8785374

mean(models$vid %in% afs.nomissing$vid)

## [1] 0.671274

Overall distribution

temp.afs = afs.nomissing
temp.afs$fA = (temp.afs$nAA*2 + temp.afs$nRA) / (2*(temp.afs$nAA + temp.afs$nRA + temp.afs$nRR))
temp.afs = acast(temp.afs, vid ~ cohort, value.var = "fA", fill = NA)
pairs(temp.afs[,cohorts.main], pch = ".")

library(corrplot)

## corrplot 0.84 loaded

corrplot.mixed(cor(temp.afs[,cohorts.main]), lower = "ellipse", upper = "number")

temp.overall_cohort.pvals = sapply(cohorts.main[1:(length(cohorts.main)-1)], function(cohort_1) {
    cohort_1_idx = which(cohorts.main == cohort_1)
    afs_1 = temp.afs[,cohort_1]
    sapply(cohorts.main[(cohort_1_idx+1):length(cohorts.main)], function(cohort_2) {
        afs_2 = temp.afs[,cohort_2]
        test = wilcox.test(afs_1 - afs_2)
        test$p.value
    })
})

temp.overall_cohort.pvals

## $mgrborig
##       gnomad         ukbb 
## 7.208864e-01 2.784435e-17 
## 
## $gnomad
##         ukbb 
## 6.889826e-05

p.adjust(unlist(temp.overall_cohort.pvals), "holm")

## mgrborig.gnomad   mgrborig.ukbb     gnomad.ukbb 
##    7.208864e-01    8.353305e-17    1.377965e-04

temp.af.gnomad = temp.afs[,"gnomad"]
temp.af.ukbb = temp.afs[,"ukbb"]
temp.af.mgrb = temp.afs[,"mgrborig"]
hist(temp.af.ukbb - temp.af.mgrb, breaks = c(-Inf, seq(-0.05, 0.05, 0.001), Inf), col = "grey", border = FALSE, xlim = c(-0.05, 0.05))

hist(temp.af.ukbb - temp.af.gnomad, breaks = c(-Inf, seq(-0.05, 0.05, 0.001), Inf), col = "grey", border = FALSE, xlim = c(-0.05, 0.05))

# Interestingly much higher AF diversity for gnomAD, despite it being a larger cohort.  Population effects?
t.test(temp.af.ukbb - temp.af.mgrb)

## 
##  One Sample t-test
## 
## data:  temp.af.ukbb - temp.af.mgrb
## t = -7.2744, df = 21047, p-value = 3.603e-13
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -0.0004276082 -0.0002460822
## sample estimates:
##     mean of x 
## -0.0003368452

t.test(temp.af.ukbb - temp.af.gnomad)

## 
##  One Sample t-test
## 
## data:  temp.af.ukbb - temp.af.gnomad
## t = -4.7358, df = 21047, p-value = 2.196e-06
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -0.0006723020 -0.0002786997
## sample estimates:
##     mean of x 
## -0.0004755008

There is a very slight but statistically significant skew in the AFs between UKBB and MGRB/gnomAD: UKBB has ever so slightly lower representation of the alt allele than both MGRB (0.0003360821 less) and gnomAD (0.0004744416 less). I suspect a subtle technical effect.

To address: is this of concern for the PRS calculations? This slight bias would be of concern if both:

1. The PRS allele effect direction was consistently skewed either to or away from the reference allele, and
2. The magnitude of sum(skew x beta) was significant relative to any inter-cohort PRS differences.

2 is difficult to address before we calculate the actual PRS distributions. 1 however we can test now.

pheno_alleles = read.csv("../data/phenotype_associated_alleles.all.csv", stringsAsFactors = FALSE)
pheno_alleles = pheno_alleles[pheno_alleles$vid %in% afs.nomissing$vid,]
# Keep only alleles with consistent effect on a phenotype class
pheno_alleles = ddply(pheno_alleles, .(class, vid), function(d) {
    if (nrow(d) > 1 && (all(d$direction == 1) || all(d$direction == -1)))
        d = d[1,,drop=FALSE]
    d
})
write.csv(pheno_alleles, "../data/phenotype_associated_alleles.filt.csv", quote = FALSE, row.names = FALSE)
pheno_alleles.tests = ddply(pheno_alleles, .(class), function(d) {
    af.gnomad = temp.afs[d$vid, "gnomad"]
    af.mgrb = temp.afs[d$vid, "mgrborig"]
    af.ukbb = temp.afs[d$vid, "ukbb"]

    daf.mgrb_gnomad = (af.mgrb - af.gnomad) * d$direction
    daf.mgrb_ukbb = (af.mgrb - af.ukbb) * d$direction

    n.mgrb_gt_gnomad.protective = sum(af.mgrb > af.gnomad & d$direction == -1)
    n.mgrb_gt_gnomad.deleterious = sum(af.mgrb > af.gnomad & d$direction == 1)
    n.gnomad_gt_mgrb.protective = sum(af.mgrb < af.gnomad & d$direction == -1)
    n.gnomad_gt_mgrb.deleterious = sum(af.mgrb < af.gnomad & d$direction == 1)

    ft.mgrb_gnomad = fisher.test(matrix(c(n.mgrb_gt_gnomad.protective, n.gnomad_gt_mgrb.protective, n.mgrb_gt_gnomad.deleterious, n.gnomad_gt_mgrb.deleterious), nrow = 2))

    n.mgrb_gt_ukbb.protective = sum(af.mgrb > af.ukbb & d$direction == -1)
    n.mgrb_gt_ukbb.deleterious = sum(af.mgrb > af.ukbb & d$direction == 1)
    n.ukbb_gt_mgrb.protective = sum(af.mgrb < af.ukbb & d$direction == -1)
    n.ukbb_gt_mgrb.deleterious = sum(af.mgrb < af.ukbb & d$direction == 1)
    ft.mgrb_ukbb = fisher.test(matrix(c(n.mgrb_gt_ukbb.protective, n.ukbb_gt_mgrb.protective, n.mgrb_gt_ukbb.deleterious, n.ukbb_gt_mgrb.deleterious), nrow = 2))

    data.frame(
        class = d$class[[1]], 
        ref_cohort = "mgrb", 
        test_cohort = c("gnomad", "ukbb"), 
        deltaaf_direction.median = c(median(daf.mgrb_gnomad), median(daf.mgrb_ukbb)),
        p.value.wilcox = c(wilcox.test(daf.mgrb_gnomad)$p.value, wilcox.test(daf.mgrb_ukbb)$p.value),
        or.fisher = c(ft.mgrb_gnomad$estimate, ft.mgrb_ukbb$estimate),
        cil.fisher = c(ft.mgrb_gnomad$conf.int[[1]], ft.mgrb_ukbb$conf.int[[1]]),
        ciu.fisher = c(ft.mgrb_gnomad$conf.int[[2]], ft.mgrb_ukbb$conf.int[[2]]),
        p.value.fisher = c(ft.mgrb_gnomad$p.value, ft.mgrb_ukbb$p.value))
})

pheno_alleles.tests$p.value.wilcox.holm = p.adjust(pheno_alleles.tests$p.value.wilcox, "holm")
pheno_alleles.tests$p.value.fisher.holm = p.adjust(pheno_alleles.tests$p.value.fisher, "holm")
pheno_alleles.tests

##            class ref_cohort test_cohort deltaaf_direction.median
## 1 anthropometric       mgrb      gnomad            -1.277496e-04
## 2 anthropometric       mgrb        ukbb            -1.653798e-05
## 3    behavioural       mgrb      gnomad             2.728057e-05
## 4    behavioural       mgrb        ukbb            -2.988239e-04
## 5       depleted       mgrb      gnomad            -3.750209e-03
## 6       depleted       mgrb        ukbb            -1.449596e-03
##   p.value.wilcox or.fisher cil.fisher ciu.fisher p.value.fisher
## 1   3.668051e-01 1.1007675  0.7340203   1.653162   6.931847e-01
## 2   8.792646e-01 1.0006054  0.6673769   1.499636   1.000000e+00
## 3   6.599423e-01 0.9837027  0.6985942   1.384911   9.333614e-01
## 4   3.107888e-01 1.1153097  0.7921750   1.570790   5.573214e-01
## 5   3.717134e-10 2.6607300  1.9391732   3.662378   2.638859e-10
## 6   3.436825e-08 2.1320342  1.5567164   2.927677   1.050530e-06
##   p.value.wilcox.holm p.value.fisher.holm
## 1        1.000000e+00        1.000000e+00
## 2        1.000000e+00        1.000000e+00
## 3        1.000000e+00        1.000000e+00
## 4        1.000000e+00        1.000000e+00
## 5        2.230280e-09        1.583315e-09
## 6        1.718413e-07        5.252648e-06

Save the allele freqs for a supp table

temp.nRR = acast(afs.nomissing, vid ~ cohort, value.var = "nRR", fill = NA)[,cohorts.main]
temp.nRA = acast(afs.nomissing, vid ~ cohort, value.var = "nRA", fill = NA)[,cohorts.main]
temp.nAA = acast(afs.nomissing, vid ~ cohort, value.var = "nAA", fill = NA)[,cohorts.main]
temp.nmissing = acast(afs.nomissing, vid ~ cohort, value.var = "nmissing", fill = NA)[,cohorts.main]
temp.AC = 2*temp.nAA + temp.nRA
temp.AN = 2*(temp.nRR + temp.nRA + temp.nAA)
temp = cbind(temp.AC, temp.AN)
colnames(temp)[1:ncol(temp.AC)] = paste("AC.", colnames(temp.AC), sep = "")
colnames(temp)[(ncol(temp.AC)+1):ncol(temp)] = paste("AN.", colnames(temp.AN), sep = "")
colnames(temp) = gsub("mgrborig", "mgrb", colnames(temp))

# Suppress generation of the file with UKBB data:
# write.csv(temp, file = "data/gwas_afs.csv", row.names = TRUE)

# We likely don't have permission to release UKBB AFs on such a broad scale, so
# generate a no UKBB set also:
write.csv(temp[,!grepl("ukbb", colnames(temp))], file = "gwas_afs_noukbb.csv", row.names = TRUE)

Individual loci

g.test = function(tbl)
{
    expected = outer(rowSums(tbl), colSums(tbl)) / sum(tbl)
    logoe = log(tbl/expected)
    logoe[tbl == 0] = 0
    stat = 2*sum(tbl*logoe)
    pchisq(stat, prod(dim(tbl)-1), lower.tail = FALSE)
}

temp.locus_cohort.pvals = ddply(afs.nomissing[afs.nomissing$vid %in% models$vid & afs.nomissing$cohort %in% cohorts.main,], .(vid), function(d) {
    nR = d$nRR*2 + d$nRA
    nA = d$nAA*2 + d$nRA
    g.test(cbind(nR, nA))
    # g.test(as.matrix(d[,c("nRR", "nRA", "nAA")]))
})
colnames(temp.locus_cohort.pvals)[2] = "p.value"
temp.locus_cohort.pvals$p.value.mtc = p.adjust(temp.locus_cohort.pvals$p.value, "BH")
# temp.locus_cohort.pvals$p.value.mtc is now calibrated for average false rejection rate 
# (ie calling a SNP population-associated when it in fact isn't).

mean(temp.locus_cohort.pvals$p.value.mtc < 0.01)

## [1] 0.4721724

temp.locus_cohort.maxdeltaaf = ddply(afs.nomissing[afs.nomissing$vid %in% models$vid & afs.nomissing$cohort %in% cohorts.main,], .(vid), function(d) {
    nR = d$nRR*2 + d$nRA
    nA = d$nAA*2 + d$nRA
    AAF = nA/(nA+nR)
    max(AAF) - min(AAF)
})
colnames(temp.locus_cohort.maxdeltaaf)[2] = "maxdeltaaaf"

temp.locus_cohort.maxdeltaaf[order(temp.locus_cohort.maxdeltaaf$maxdeltaaaf),]

##                   vid  maxdeltaaaf
## 635   20:41851935:G:A 4.804901e-05
## 175     11:244552:A:G 5.472387e-04
## 698   3:163838015:A:C 5.854864e-04
## 848   5:176517326:T:C 6.520533e-04
## 865    5:58337481:T:G 6.896540e-04
## 581   2:232268312:T:C 8.648204e-04
## 64    1:242034263:A:G 8.926576e-04
## 561    2:19942473:G:A 8.944422e-04
## 800    4:61995613:A:G 9.804085e-04
## 344   15:32993111:C:T 1.013646e-03
## 126   10:12943973:C:T 1.036166e-03
## 431   17:43216281:C:T 1.120399e-03
## 940    6:43711981:T:C 1.242711e-03
## 87     1:65010606:T:G 1.410640e-03
## 1094   9:22062134:G:T 1.487932e-03
## 960    6:81792063:G:T 1.508864e-03
## 369   15:72842705:G:A 1.511067e-03
## 734    3:62133492:G:A 1.517305e-03
## 771   4:147993702:A:G 1.550150e-03
## 50    1:215046892:G:A 1.631525e-03
## 46    1:203766331:A:G 1.651584e-03
## 792    4:39503196:A:G 1.678110e-03
## 816   5:108625324:C:A 1.746323e-03
## 1095   9:22102165:C:T 1.753972e-03
## 35     1:17308254:T:C 1.809376e-03
## 465   18:19450303:A:G 1.867013e-03
## 463     17:800593:T:C 1.957503e-03
## 666   21:45867411:G:A 1.968592e-03
## 291   13:55934157:A:G 1.984521e-03
## 1114   9:99203606:T:C 2.015219e-03
## 547   2:179786068:T:C 2.214285e-03
## 222  12:125441159:T:C 2.246113e-03
## 365   15:67455630:C:T 2.312045e-03
## 447   17:64783539:C:T 2.316572e-03
## 1082  9:118826916:G:A 2.361107e-03
## 385   15:98615560:C:T 2.370182e-03
## 716   3:190815978:A:G 2.376253e-03
## 18    1:151259043:C:T 2.419978e-03
## 967   7:107259721:T:C 2.424953e-03
## 935    6:36659932:C:T 2.450101e-03
## 688   3:136107549:G:A 2.505036e-03
## 14     1:14105298:G:A 2.546910e-03
## 887   6:118569679:T:G 2.552647e-03
## 1011  8:110115372:C:T 2.598390e-03
## 158   11:11563879:C:T 2.615930e-03
## 301   13:80618435:A:G 2.616690e-03
## 982   7:148629759:C:T 2.621543e-03
## 719    3:27416013:C:T 2.622335e-03
## 552   2:191227755:A:G 2.638522e-03
## 480   18:57323149:C:A 2.650551e-03
## 1023  8:128106880:A:C 2.808417e-03
## 37    1:177279412:G:A 2.814433e-03
## 808    4:82204091:A:G 2.816117e-03
## 953    6:75452066:T:C 2.865091e-03
## 506   19:42683964:C:T 2.865981e-03
## 818   5:113748571:C:T 2.886389e-03
## 639   20:50141264:T:C 2.900362e-03
## 900   6:149608874:G:A 2.955662e-03
## 1013  8:115698881:G:A 2.962404e-03
## 485   18:77222862:T:G 2.971526e-03
## 333   14:90636206:G:A 3.008568e-03
## 210  12:112059557:C:T 3.037502e-03
## 577   2:219903723:C:T 3.051369e-03
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## 85     1:59653742:A:G 1.770383e-02
## 355   15:58650355:C:T 1.770944e-02
## 1008   7:92659160:C:T 1.771433e-02
## 996    7:27976563:G:A 1.775104e-02
## 573   2:218296508:C:T 1.777715e-02
## 981   7:145720467:A:G 1.778719e-02
## 167   11:14404825:C:T 1.786384e-02
## 359   15:62379971:A:G 1.788374e-02
## 413   16:89875710:A:C 1.791630e-02
## 765    4:12963574:G:A 1.793358e-02
## 32    1:170346164:C:T 1.793654e-02
## 735    3:63967900:A:G 1.794274e-02
## 178   11:35972672:G:A 1.807000e-02
## 850   5:179730843:A:G 1.809441e-02
## 980   7:144074929:G:A 1.809577e-02
## 898   6:142703877:G:A 1.810963e-02
## 216  12:116391296:T:C 1.811836e-02
## 354   15:54455757:T:C 1.812501e-02
## 1030  8:130723728:A:G 1.816356e-02
## 375   15:78816057:G:T 1.818666e-02
## 124  10:126383088:C:A 1.820138e-02
## 106  10:104604916:T:G 1.822156e-02
## 509   19:45415713:G:A 1.827054e-02
## 1102   9:86661654:C:T 1.827304e-02
## 10    1:118854698:G:A 1.829201e-02
## 963    6:84277037:C:A 1.829773e-02
## 632   20:40534202:G:A 1.833764e-02
## 130   10:27890831:A:G 1.839150e-02
## 557   2:198077877:A:G 1.843233e-02
## 516    19:7244233:A:C 1.844957e-02
## 1027  8:128424792:A:G 1.851813e-02
## 601    2:42462930:A:G 1.855264e-02
## 373   15:78686823:A:G 1.866659e-02
## 2      1:10566215:A:G 1.871633e-02
## 476   18:46657358:C:T 1.872113e-02
## 341  15:101632867:G:A 1.877734e-02
## 231   12:24784139:G:A 1.885831e-02
## 362   15:66867861:A:G 1.889948e-02
## 603    2:43463637:T:C 1.893412e-02
## 276   13:23371474:T:C 1.898917e-02
## 824   5:132949899:A:G 1.899640e-02
## 446    17:6474096:C:T 1.899675e-02
## 54    1:218975475:G:A 1.900778e-02
## 248   12:58256714:T:G 1.905047e-02
## 435   17:47402807:C:T 1.906915e-02
## 615    2:68495002:G:A 1.907063e-02
## 331   14:75038472:T:C 1.907516e-02
## 205   11:85867875:A:G 1.910143e-02
## 65    1:243471192:A:G 1.913178e-02
## 1063   8:93643870:C:T 1.914344e-02
## 183   11:59923508:A:G 1.914429e-02
## 657   21:30567941:G:T 1.917545e-02
## 285   13:49201040:T:G 1.922188e-02
## 1109   9:97429160:A:G 1.923755e-02
## 1098   9:33026572:T:C 1.930564e-02
## 542   2:174815898:A:C 1.931885e-02
## 779   4:163337191:C:T 1.933543e-02
## 1090  9:138698196:G:A 1.940762e-02
## 722    3:38624343:A:G 1.942865e-02
## 391    16:2248888:T:C 1.943051e-02
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## 884   6:117210052:T:C 1.951065e-02
## 275   13:23329181:G:A 1.954871e-02
## 1070  9:108901049:C:T 1.955231e-02
## 116  10:116828824:T:G 1.963734e-02
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## 1042   8:19493786:T:C 1.970229e-02
## 361   15:63439186:C:T 1.970537e-02
## 886   6:117868051:T:C 1.978912e-02
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## 24    1:154834183:G:A 1.993863e-02
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## 1035  8:141729463:C:T 2.881498e-02
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## 571   2:217935116:T:C 2.953341e-02
## 668   22:19983213:C:T 2.954049e-02
## 108  10:105324774:C:T 2.955258e-02
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## 532   2:145645775:G:A 2.980645e-02
## 857    5:33989518:C:T 2.987911e-02
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## 17    1:149938898:T:C 3.104603e-02
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## 793    4:41261500:T:C 3.129284e-02
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## 582   2:232322779:G:A 3.146841e-02
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## 304   13:87001719:T:C 3.152685e-02
## 593    2:28635740:T:C 3.163465e-02
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## 526   2:136187345:C:T 3.169046e-02
## 905   6:152437016:T:C 3.183736e-02
## 925    6:28747902:T:C 3.196243e-02
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## 240    12:4942953:T:G 3.219421e-02
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## 725    3:46600520:A:G 3.646873e-02
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## 21    1:154404406:A:C 3.670752e-02
## 748   4:106216205:T:C 3.713331e-02
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## 1112   9:98265780:C:T 3.781516e-02
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## 437   17:53209774:A:C 3.849144e-02
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## 713   3:186004526:T:C 3.933196e-02
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## 860     5:4012694:G:A 3.986729e-02
## 139    10:5886734:C:T 3.987780e-02
## 644   20:60920887:G:A 4.081819e-02
## 902   6:151942194:T:G 4.149024e-02
## 272   13:21570246:T:G 4.210229e-02
## 591    2:26924823:A:C 4.308281e-02
## 637   20:48316027:C:T 4.369981e-02
## 924    6:26200677:A:G 4.507931e-02
## 226   12:18040964:A:C 4.572318e-02
## 746   4:106061534:C:A 4.717647e-02
## 752   4:111586468:A:G 4.918761e-02
## 225   12:14520701:A:G 4.978408e-02
## 823   5:131585958:A:G 5.031346e-02
## 518    2:10178479:C:T 5.415964e-02
## 313   14:32981484:G:A 5.612800e-02
## 754   4:111706275:A:G 5.732161e-02

hist(temp.locus_cohort.maxdeltaaf$maxdeltaaaf)

# On the basis of this histogram, set a max delta aaf threshold of
# 4%.  Drop loci with a delta AAF greater than this.
mean(temp.locus_cohort.maxdeltaaf$maxdeltaaaf < 0.04)

## [1] 0.9874327

temp.sel_loci = temp.locus_cohort.maxdeltaaf$vid[temp.locus_cohort.maxdeltaaf$maxdeltaaaf < 0.04]
afs = afs[afs$vid %in% temp.sel_loci,]
models = models[models$vid %in% temp.sel_loci,]

Attempt to model the cohort AAF differences.

temp.afs = afs
temp.afs$fA = (temp.afs$nAA*2 + temp.afs$nRA) / (2*(temp.afs$nAA + temp.afs$nRA + temp.afs$nRR))
temp.afs = acast(temp.afs, vid ~ cohort, value.var = "fA", fill = NA)

temp.af.gnomad = temp.afs[,"gnomad"]
temp.af.ukbb = temp.afs[,"ukbb"]
temp.af.mgrb = temp.afs[,"mgrborig"]

logit = function(p) log(p) - log(1-p)

pairs(cbind(mgrb = logit(temp.af.mgrb), ukbb = logit(temp.af.ukbb), delta = logit(temp.af.ukbb) - logit(temp.af.mgrb)), pch = ".")

pairs(cbind(mgrb = temp.af.mgrb, ukbb = temp.af.ukbb, delta = temp.af.ukbb - temp.af.mgrb), pch = ".")

pairs(cbind(mgrb = temp.af.mgrb, ukbb = temp.af.ukbb, deltastd = (temp.af.ukbb - temp.af.mgrb)/sqrt(temp.af.ukbb*(1-temp.af.ukbb))), pch = ".")

pairs(cbind(mgrb = logit(temp.af.mgrb), ukbb = logit(temp.af.ukbb), deltastd = (temp.af.ukbb - temp.af.mgrb)/sqrt(temp.af.ukbb*(1-temp.af.ukbb))), pch = ".")

hist((temp.af.ukbb - temp.af.mgrb)/sqrt(temp.af.mgrb*(1-temp.af.mgrb)), breaks = 25, col = "grey")

pairs(cbind(mgrb = logit(temp.af.mgrb), gnomad = logit(temp.af.gnomad), delta = logit(temp.af.gnomad) - logit(temp.af.mgrb)), pch = ".")

pairs(cbind(mgrb = temp.af.mgrb, gnomad = temp.af.gnomad, delta = temp.af.gnomad - temp.af.mgrb), pch = ".")

pairs(cbind(mgrb = temp.af.mgrb, gnomad = temp.af.gnomad, deltastd = (temp.af.gnomad - temp.af.mgrb)/sqrt(temp.af.gnomad*(1-temp.af.gnomad))), pch = ".")

pairs(cbind(mgrb = logit(temp.af.mgrb), gnomad = logit(temp.af.gnomad), deltastd = (temp.af.gnomad - temp.af.mgrb)/sqrt(temp.af.gnomad*(1-temp.af.gnomad))), pch = ".")

hist((temp.af.gnomad - temp.af.mgrb)/sqrt(temp.af.mgrb*(1-temp.af.mgrb)), breaks = 25, col = "grey")

# Looks like a sd norm makes the allele frequency difference largely independent of AAF.
# Therefore we can characterise the distribution of this normalised frequency difference
# and sample from it without needing to condition on the allele frequency.
# With > 20k loci we may as well just bootstrap directly instead of fitting a distribution
# and sampling.
norm_delta_aaf.mgrb_ukbb = (temp.af.mgrb - temp.af.ukbb)/sqrt(temp.af.ukbb*(1-temp.af.ukbb))
norm_delta_aaf.mgrb_gnomad = (temp.af.mgrb - temp.af.gnomad)/sqrt(temp.af.gnomad*(1-temp.af.gnomad))

PRS calculation

Perform a ‘stress test’ for the PRS as suggested by Greg. We wish to show here that the PRS differences between MGRB and UKBB, or MGRB and GnomAD, are unlikely to be simply due to drift. To do this, we simulate hypothetical MGRB cohorts derived from either UKBB or GnomAD, that are consistent with the drift-only hypothesis.

The model:

POPULATION:    UK  --drift & ethnicity-->  Australian  --selection-->  Australian Wellderly
               |                               |                                |
               V                               V                                V
SAMPLE:       UKBB                        Australian*                          MGRB

The ideal comparison is the Australian sample vs MGRB. However, this Australian sample is not available. We simulate it by derivation from the UKBB sample, based on the MGRB - UKBB allele frequencies, on the assumption that the distribution of MAF_MGRB - MAF_UKBB will be very close to the distribution of MAF_Aus - MAF_UKBB. This is reasonable if we suppose that relatively few loci are linked to depleted MGRB phenotypes.

Proceed as follows:

1. Calculate normalised MGRB - UKBB AAF differences using observed AFs. As these AFs were sampled, they already incorporate sampling error, and we do not need to perform an additional sampling stage later. \(D_i = \frac{F_{MGRB}_i - F_{UKBB}_i}{\sqrt{(F_{UKBB}_i)*(1-F_{UKBB}_i)}}\)
2. Calculate expected MGRB PRS scores using observed AFs.
3. For each bootstrap iteration \(k\):
   1. Take UKBB PRS AFs.
   2. Sample hypothetical MGRB AFs as \[f_{MGRB}^{(k)}_i = f_{UKBB}_i + d^{(k)}_i*\sqrt{(f_{UKBB}_i)*(1-f_{UKBB}_i)}\] where \(d^{(k)} \~ d\).
   3. Calculate expected MGRB PRS scores
4. Compare the permuted MGRB scores (reflective of the null of population drift-only differences) to the observed UKBB and MGRB scores.

stressboot.nboot = 100000
stressboot.cohorts = c("ukbb", "gnomad")

temp.afs.nomissing.modelonly = afs.nomissing[afs.nomissing$vid %in% models$vid,]
temp.afs.nomissing.modelonly$aaf = (temp.afs.nomissing.modelonly$nAA + 0.5*temp.afs.nomissing.modelonly$nRA)/(temp.afs.nomissing.modelonly$nAA + temp.afs.nomissing.modelonly$nRA + temp.afs.nomissing.modelonly$nRR)

stressboot.afmat.orig = acast(temp.afs.nomissing.modelonly, vid ~ cohort, value.var = "aaf")
stressboot.afmat.orig = stressboot.afmat.orig[,c("mgrborig", stressboot.cohorts)]
stressboot.models = acast(models, id ~ vid, value.var = "coef")
stressboot.models[is.na(stressboot.models)] = 0
stressboot.models = stressboot.models[,rownames(stressboot.afmat.orig)]
stopifnot(rownames(stressboot.afmat.orig) == colnames(stressboot.models))

stressboot.scores.orig = (2 * stressboot.models %*% stressboot.afmat.orig) / rowSums(stressboot.models != 0)
names(dimnames(stressboot.scores.orig)) = c("model", "cohort")

stressboot.normafdelta = list("aus_from_ukbb" = norm_delta_aaf.mgrb_ukbb, "aus_from_gnomad" = norm_delta_aaf.mgrb_gnomad)

stressboot.tasks = expand.grid(bootiter = 1:stressboot.nboot, deriv_cohort = paste("aus_from_", stressboot.cohorts, sep = ""))
stressboot.pb = progress_estimated(nrow(stressboot.tasks))

stressboot.scores.boot = aperm(daply(stressboot.tasks, .(deriv_cohort, bootiter), function(d) {
    update_progress(stressboot.pb)
    stopifnot(nrow(d) == 1)
    source_cohort = gsub("^aus_from_", "", d$deriv_cohort)
    bootiter = d$bootiter
    this.normdelta = stressboot.normafdelta[[d$deriv_cohort]]
    set.seed(314159+bootiter-1)   # Will --> linked normdelta samples between the cohorts

    this.delta = sample(this.normdelta, nrow(stressboot.afmat.orig), replace = TRUE)
    this.aus_sim_af = stressboot.afmat.orig[,source_cohort] + this.delta*sqrt(stressboot.afmat.orig[,source_cohort]*(1-stressboot.afmat.orig[,source_cohort]))
    this.aus_sim_af = pmax(0, pmin(1, this.aus_sim_af))

    (2 * stressboot.models %*% this.aus_sim_af) / rowSums(stressboot.models != 0)
}), c(3, 1, 2))
names(dimnames(stressboot.scores.boot))[1] = "model"

saveRDS(stressboot.afmat.orig, "stressboot_afmat_orig.rds")
saveRDS(stressboot.models, "stressboot_models.rds")
print(rowSums(stressboot.models != 0))

##          AF:Lubitz:10.1161/CIRCULATIONAHA.116.024143 
##                                                  390 
##            AlzheimersDisease:Lambert:10.1038/ng.2802 
##                                                   12 
##         BreastCancer:Michailidou:10.1038/nature24284 
##                                                   64 
##       ColorectalCancer:Schumacher:10.1038/ncomms8138 
##                                                   35 
##                   DiastolicBP:Warren:10.1038/ng.3768 
##                                                   28 
##           EOCAD:Theriault:10.1161/circgen.117.001849 
##                                                   93 
##                          Height:Wood:10.1038/ng.3097 
##                                                  408 
##                         Melanoma:Law:10.1038/ng.3373 
##                                                   11 
## ProstateCancer:Hoffmann:10.1158/2159-8290.CD-15-0315 
##                                                   17 
##                 PulsePressure:Warren:10.1038/ng.3768 
##                                                   21 
##      ShortHealthspan:Zenin:10.1038/s42003-019-0290-0 
##                                                    3 
##    ShortParentalLifespan:Timmers:10.7554/eLife.39856 
##                                                    7 
##                    SystolicBP:Warren:10.1038/ng.3768 
##                                                   14

print(dim(stressboot.scores.orig))

## [1] 13  3

# Convert to data frames for ggplot
stressboot.dfs = list(original = melt(stressboot.scores.orig[,stressboot.cohorts]), boot = melt(stressboot.scores.boot))
temp.mgrb_scores = stressboot.scores.orig[,"mgrborig"]
temp.ukbb_sd = apply(stressboot.scores.boot[,"aus_from_ukbb",], 1, sd)   # Get SDs from UKBB to normalise scores for plotting
stressboot.dfs$original$value.mgrb = temp.mgrb_scores[stressboot.dfs$original$model]
stressboot.dfs$boot$value.mgrb = temp.mgrb_scores[stressboot.dfs$boot$model]
stressboot.dfs$original$value.rel = stressboot.dfs$original$value - stressboot.dfs$original$value.mgrb
stressboot.dfs$boot$value.rel = stressboot.dfs$boot$value - stressboot.dfs$boot$value.mgrb
stressboot.dfs$summary = ddply(stressboot.dfs$boot, .(model, deriv_cohort), function(d) {
    mean.rel = mean(d$value.rel)
    ci.rel = quantile(d$value.rel, c(0.025, 0.975))
    nneg = sum(d$value.rel < 0)
    npos = sum(d$value.rel > 0)
    p.value = 2 * (min(nneg, npos) + 0.5) / (nrow(d)+1)
    c(p.value = p.value, mean.rel = mean.rel, lcl.rel = ci.rel[[1]], ucl.rel = ci.rel[[2]], nneg = nneg, npos = npos) })
stressboot.dfs$summary$p.value.holm = p.adjust(stressboot.dfs$summary$p.value, "holm")
stressboot.dfs$summary$p.value.BH = p.adjust(stressboot.dfs$summary$p.value, "BH")
stressboot.dfs$summary$mean.rel.norm = stressboot.dfs$summary$mean.rel / temp.ukbb_sd[stressboot.dfs$summary$model]
stressboot.dfs$summary$lcl.rel.norm = stressboot.dfs$summary$lcl.rel / temp.ukbb_sd[stressboot.dfs$summary$model]
stressboot.dfs$summary$ucl.rel.norm = stressboot.dfs$summary$ucl.rel / temp.ukbb_sd[stressboot.dfs$summary$model]

stressboot.dfs$summary$plot_cohort = c("aus_from_ukbb" = "UKBB", "aus_from_gnomad" = "gnomAD")[stressboot.dfs$summary$deriv_cohort]
library(ggplot2)
ggplot(stressboot.dfs$summary, aes(x = model, y = mean.rel.norm, ymin = lcl.rel.norm, ymax = ucl.rel.norm, col = plot_cohort, group = plot_cohort)) + 
    geom_point(position = position_dodge(width = 0.7), size = 2) + geom_errorbar(position = position_dodge(width = 0.7), width = 0.3, lwd = 1) + 
    geom_hline(yintercept = 0, lty = "dashed") + 
    labs(y = "Polygenic score relative to MGRB, normalised", x = "Polygenic model", col = "Comparison cohort") + theme_bw() + coord_flip()

for (i in 1:nrow(stressboot.dfs$summary))
{
    try(
    dafplot(
        afs1 = afs.nomissing[afs.nomissing$cohort == "mgrborig",], 
        afs2 = afs.nomissing[afs.nomissing$cohort == gsub("^aus_from_", "", stressboot.dfs$summary$deriv_cohort[i]),], 
        model = models[models$id == stressboot.dfs$summary$model[i],],
        main = stressboot.dfs$summary$model[i],
        xlab = "",
        # xlab = expression(paste("PRS ", beta)),
        ylab = sprintf("MAF MGRB - %s", gsub("^aus_from_", "", stressboot.dfs$summary$deriv_cohort[i])),
        mar = c(9, 4, 4, 2)+0.1,
        sub = sprintf("\ndelta_mean=%.3e  (%.3e-%.3e)\np.raw=%.4f  p.holm=%.4f  p.bh=%.4f", stressboot.dfs$summary$mean.rel[i], stressboot.dfs$summary$lcl.rel[i], stressboot.dfs$summary$ucl.rel[i], stressboot.dfs$summary$p.value[i], stressboot.dfs$summary$p.value.holm[i], stressboot.dfs$summary$p.value.BH[i]))
    )
}

sessionInfo()

## R version 3.5.3 (2019-03-11)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18362)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_Australia.1252  LC_CTYPE=English_Australia.1252   
## [3] LC_MONETARY=English_Australia.1252 LC_NUMERIC=C                      
## [5] LC_TIME=English_Australia.1252    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggplot2_3.1.1          kableExtra_1.1.0       knitr_1.22            
##  [4] knitrProgressBar_1.1.0 corrplot_0.84          plyr_1.8.4            
##  [7] reshape2_1.4.3         rmarkdown_1.12         RevoUtils_11.0.3      
## [10] RevoUtilsMath_11.0.0  
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.1        highr_0.8         compiler_3.5.3   
##  [4] pillar_1.3.1      R.methodsS3_1.7.1 tools_3.5.3      
##  [7] digest_0.6.18     gtable_0.3.0      evaluate_0.13    
## [10] tibble_2.1.1      viridisLite_0.3.0 pkgconfig_2.0.2  
## [13] rlang_0.3.4       rstudioapi_0.10   yaml_2.2.0       
## [16] xfun_0.6          withr_2.1.2       dplyr_0.8.0.1    
## [19] stringr_1.4.0     httr_1.4.0        xml2_1.2.0       
## [22] hms_0.4.2         tidyselect_0.2.5  grid_3.5.3       
## [25] webshot_0.5.1     glue_1.3.1        R6_2.3.0         
## [28] purrr_0.3.2       readr_1.3.1       magrittr_1.5     
## [31] scales_1.0.0      htmltools_0.3.6   assertthat_0.2.1 
## [34] rvest_0.3.3       colorspace_1.4-1  labeling_0.3     
## [37] stringi_1.4.3     lazyeval_0.2.2    munsell_0.5.0    
## [40] crayon_1.3.4      R.oo_1.22.0